Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title: this is an example of a piecewise growth
model for a continuous outcome
montecarlo:
names = y1-y5;
nobs = 500;
nreps = 1;
save = ex6.11.dat;
model population:
i s1 | y1@0 y2@1 y3@2 y4@2 y5@2;
i s2 | y1@0 y2@0 y3@0 y4@1 y5@2;
y1-y5*.5;
[i*.5 s1*1 s2*2];
i*1; s1-s2*.2;
model:
i s1 | y1@0 y2@1 y3@2 y4@2 y5@2;
i s2 | y1@0 y2@0 y3@0 y4@1 y5@2;
y1-y5*.5;
[i*.5 s1*1 s2*2];
i*1; s1-s2*.2;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a piecewise growth
model for a continuous outcome
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 5
Number of independent variables 0
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5
Continuous latent variables
I S1 S2
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.443 1.584 2.595 4.535 6.535
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.367
Y2 0.963 1.732
Y3 0.906 1.408 2.318
Y4 0.976 1.422 1.797 2.491
Y5 1.030 1.480 1.824 2.252 3.269
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.626 1.000
Y3 0.509 0.703 1.000
Y4 0.529 0.684 0.748 1.000
Y5 0.487 0.622 0.662 0.789 1.000
MODEL FIT INFORMATION
Number of Free Parameters 14
Loglikelihood
H0 Value
Mean -3706.171
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3706.171 -3706.171
0.980 0.000 -3706.171 -3706.171
0.950 0.000 -3706.171 -3706.171
0.900 0.000 -3706.171 -3706.171
0.800 0.000 -3706.171 -3706.171
0.700 0.000 -3706.171 -3706.171
0.500 0.000 -3706.171 -3706.171
0.300 0.000 -3706.171 -3706.171
0.200 0.000 -3706.171 -3706.171
0.100 0.000 -3706.171 -3706.171
0.050 0.000 -3706.171 -3706.171
0.020 0.000 -3706.171 -3706.171
0.010 0.000 -3706.171 -3706.171
H1 Value
Mean -3703.549
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3703.549 -3703.549
0.980 0.000 -3703.549 -3703.549
0.950 0.000 -3703.549 -3703.549
0.900 0.000 -3703.549 -3703.549
0.800 0.000 -3703.549 -3703.549
0.700 0.000 -3703.549 -3703.549
0.500 0.000 -3703.549 -3703.549
0.300 0.000 -3703.549 -3703.549
0.200 0.000 -3703.549 -3703.549
0.100 0.000 -3703.549 -3703.549
0.050 0.000 -3703.549 -3703.549
0.020 0.000 -3703.549 -3703.549
0.010 0.000 -3703.549 -3703.549
Information Criteria
Akaike (AIC)
Mean 7440.342
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7440.342 7440.342
0.980 0.000 7440.342 7440.342
0.950 0.000 7440.342 7440.342
0.900 0.000 7440.342 7440.342
0.800 0.000 7440.342 7440.342
0.700 0.000 7440.342 7440.342
0.500 0.000 7440.342 7440.342
0.300 0.000 7440.342 7440.342
0.200 0.000 7440.342 7440.342
0.100 0.000 7440.342 7440.342
0.050 0.000 7440.342 7440.342
0.020 0.000 7440.342 7440.342
0.010 0.000 7440.342 7440.342
Bayesian (BIC)
Mean 7499.346
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7499.346 7499.346
0.980 0.000 7499.346 7499.346
0.950 0.000 7499.346 7499.346
0.900 0.000 7499.346 7499.346
0.800 0.000 7499.346 7499.346
0.700 0.000 7499.346 7499.346
0.500 0.000 7499.346 7499.346
0.300 0.000 7499.346 7499.346
0.200 0.000 7499.346 7499.346
0.100 0.000 7499.346 7499.346
0.050 0.000 7499.346 7499.346
0.020 0.000 7499.346 7499.346
0.010 0.000 7499.346 7499.346
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 7454.909
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7454.909 7454.909
0.980 0.000 7454.909 7454.909
0.950 0.000 7454.909 7454.909
0.900 0.000 7454.909 7454.909
0.800 0.000 7454.909 7454.909
0.700 0.000 7454.909 7454.909
0.500 0.000 7454.909 7454.909
0.300 0.000 7454.909 7454.909
0.200 0.000 7454.909 7454.909
0.100 0.000 7454.909 7454.909
0.050 0.000 7454.909 7454.909
0.020 0.000 7454.909 7454.909
0.010 0.000 7454.909 7454.909
Chi-Square Test of Model Fit
Degrees of freedom 6
Mean 5.244
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.872 5.244
0.980 1.000 1.134 5.244
0.950 1.000 1.635 5.244
0.900 1.000 2.204 5.244
0.800 1.000 3.070 5.244
0.700 1.000 3.828 5.244
0.500 0.000 5.348 5.244
0.300 0.000 7.231 5.244
0.200 0.000 8.558 5.244
0.100 0.000 10.645 5.244
0.050 0.000 12.592 5.244
0.020 0.000 15.033 5.244
0.010 0.000 16.812 5.244
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 1.000
CFI/TLI
CFI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
TLI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
SRMR (Standardized Root Mean Square Residual)
Mean 0.010
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
I |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S1 |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
S2 |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
S1 WITH
I 0.000 -0.0291 0.0000 0.0494 0.0008 1.000 0.000
S2 WITH
I 0.000 0.0594 0.0000 0.0362 0.0035 1.000 0.000
S1 0.000 -0.0309 0.0000 0.0261 0.0010 1.000 0.000
Means
I 0.500 0.4622 0.0000 0.0516 0.0014 1.000 1.000
S1 1.000 1.0714 0.0000 0.0298 0.0051 0.000 1.000
S2 2.000 1.9573 0.0000 0.0304 0.0018 1.000 1.000
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
I 1.000 0.9846 0.0000 0.1002 0.0002 1.000 1.000
S1 0.200 0.2396 0.0000 0.0374 0.0016 1.000 1.000
S2 0.200 0.2191 0.0000 0.0416 0.0004 1.000 1.000
Residual Variances
Y1 0.500 0.3944 0.0000 0.0765 0.0111 1.000 1.000
Y2 0.500 0.5251 0.0000 0.0431 0.0006 1.000 1.000
Y3 0.500 0.5013 0.0000 0.0682 0.0000 1.000 1.000
Y4 0.500 0.4832 0.0000 0.0479 0.0003 1.000 1.000
Y5 0.500 0.5587 0.0000 0.1030 0.0034 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.136E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
I S1 S2
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
Y5 0 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
Y5 0 0 0 0 5
ALPHA
I S1 S2
________ ________ ________
6 7 8
BETA
I S1 S2
________ ________ ________
I 0 0 0
S1 0 0 0
S2 0 0 0
PSI
I S1 S2
________ ________ ________
I 9
S1 10 11
S2 12 13 14
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
I S1 S2
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 2.000 1.000
Y5 1.000 2.000 2.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
ALPHA
I S1 S2
________ ________ ________
0.500 1.000 2.000
BETA
I S1 S2
________ ________ ________
I 0.000 0.000 0.000
S1 0.000 0.000 0.000
S2 0.000 0.000 0.000
PSI
I S1 S2
________ ________ ________
I 1.000
S1 0.000 0.200
S2 0.000 0.000 0.200
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
I S1 S2
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 2.000 1.000
Y5 1.000 2.000 2.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
ALPHA
I S1 S2
________ ________ ________
0.500 1.000 2.000
BETA
I S1 S2
________ ________ ________
I 0.000 0.000 0.000
S1 0.000 0.000 0.000
S2 0.000 0.000 0.000
PSI
I S1 S2
________ ________ ________
I 1.000
S1 0.000 0.200
S2 0.000 0.000 0.200
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Save file
ex6.11.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:14
Ending Time: 22:24:14
Elapsed Time: 00:00:00
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